Adding a vent to the roof wiil require a vent kit associated for the type of tiles you have diffence in prices if your not experienced you will need a roofer possibly scaffolding a crawler ladder all which depend on height of the roof.
Vent bathroom fan through roof or wall.
This involves running ductwork from the fan usually though an attic and out through the roof.
Going to the soffet is 12 feet.
From up on the roof use a jigsaw or reciprocating saw to cut a 4 in.
Typically an exhaust fan that is vented through the roof has a roof hood or roof cap which allows air to exhaust but provides protection from wind blown rain.
It is because of this that many builders tend to advise against this method.
If your exterior siding is vinyl or fiber cement you will have an easier time cutting the hole.
If you want to vent a bathroom fan through an exterior wall you will have to cut a 3 inch or 4 inch hole with a hole saw drill bit.
Will be usually fed.
Depending on the location of the bathroom it may be easy to vent the exhaust fan through the roof.
The fan will need to be an inline fan with ducting and a grill in the bathroom.
Try to keep it close to the fan location.
Broan sells an inexpensive model which is probably available at any big box store.
Leave the drill bit sticking through the roof so you can find the hole.
Choice is go up to roof 5 6 feet or out the present vent 15 18 feet with insulated pipe or shorten the line by going straight to side of home but this requires going up high with latter to drill a new vent hole as tight quarters in attic prevent drilling from attic.